A089792 a(n) = n-(exponent of highest power of 3 dividing n!).

0, 1, 2, 2, 3, 4, 4, 5, 6, 5, 6, 7, 7, 8, 9, 9, 10, 11, 10, 11, 12, 12, 13, 14, 14, 15, 16, 14, 15, 16, 16, 17, 18, 18, 19, 20, 19, 20, 21, 21, 22, 23, 23, 24, 25, 24, 25, 26, 26, 27, 28, 28, 29, 30, 28, 29, 30, 30, 31, 32, 32, 33, 34, 33

Offset

0,3

Comments

The exponent of the highest power of 3 dividing binomial(n,k) is given by a(k)+a(n-k)-a(n).

Links

Table of n, a(n) for n=0..63.

Formula

a(n) = a(n-1)+1-A007949(n).

a(n) = log(denominator(n!/3^n))/log(3); a(n) = log_3(A125824(n)). - Paul Barry, Apr 02 2007

a(n) = n - A054861(n).

Mathematica

Table[n-IntegerExponent[n!, 3], {n, 0, 70}] (* Harvey P. Dale, Aug 09 2015 *)

Prog

(PARI) vector(70, n, n--; n-valuation(n!, 3)) \\ Michel Marcus, Aug 19 2015

Crossrefs

Cf. A007949, A054861, A125824.

Sequence in context: A168560 A333942 A065361 * A081608 A096532 A335380

Adjacent sequences: A089789 A089790 A089791 * A089793 A089794 A089795

Keyword

easy,nonn

Author

Paul Boddington, Jan 09 2004

Status

approved